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1. Field of the Invention
This invention related to an apparatus and method for imaging in either homogeneous, or layered, or porous media. The media may be fluid or solid, the imaging energy may be electromagnetic, elastic (seismic-like energy) or acoustic (sound/ultrasound energy). Furthermore, the ambient media (in which the object to be imaged is embedded) may have layering (such as stratigraphic layering, or ocean velocity layers, or layering of composites in nondestructive imaging applications) or consist or porous material (either sedimentary deposits or composites in nondestructive testing).
2. The Prior Art
It has long been known that elastic, electromagnetic or acoustic waves in homogeneous and layered environments in the frequency range of a fraction of a cycle per second up to hundreds of millions of cycles per second and higher can be propagated through many solids and liquids. Elastic waves are waves that propagate through solids, and have components of particle motion both parallel (longitudinal, or pressure, wave) and perpendicular (shear wave) to the direction of propagation of the wave energy itself. In contrast to this, acoustic waves are those waves that generate particle motion that is exclusively parallel to the propagation of wave energy. Electromagnetic waves have components of variation of field strength solely in the direction perpendicular to the direction of propagation. All of these types of waves may be used to image the acoustic longitudinal wavespeed and absorption, the electromagnetic wavespeed and absorption, the shear wavespeed, and the density of the material through which the wave energy has travelled.
It is also known that scattering is produced not only by spatial fluctuations in acoustic impedance, which is the product of mass density times wavespeed, but also by independent fluctuations in electromagnetic permeability, permittivity and conductivity, elastic compressibility, shear modulus, density, and absorption. These lead to variations in phase speed (which is the speed of propagation of fronts of constant phase) and in impedance (for the electromagnetic case, the ratio of the electric to the magnetic field strength). The net property of an object which describes the phenomenon of scattering in a given modality, is called the "scattering potential".
Other imaging methods have been applied to one or the other modality, or restricted to acoustic or elastic media, the method described in this patent is applicable to any type of wave motion, whether electromagnetic, elastic (including shear wave effects) or acoustic (scalar approximation valid in liquid and gases). Furthermore, the ambient media may have some forms of structure (layering) or microstructure (porosity) relevant to the medical, geophysical, or nondestructive imaging applications envisioned for this technology. In the prior art the presence of this layering or porosity has greatly diminished the effectiveness of the imaging program. The method of this patent minimizes the obscuring effect of such structures in the ambient media. In addition, we have made several changes to the previous U.S. Pat. No. 4,662,222 that significantly extend the applicability and speed of our algorithm. These changes are described, in part, below:
As discussed in U.S. Pat. No. 4,662,222, by one of the present authors, these principles can be used to image scattering bodies within a given medium. Some definitions will clarify the procedures and methods used:
The direct or forward scattering problem is concerned with a determination of the scattered energy or fields when the elastic or electromagnetic properties of the scattering potential are known.
The inverse scattering problem, by contrast, consists in the use of scattered electromagnetic, elastic, or acoustic waves to determine the internal material properties of objects embedded in a known (ambient) medium. An incident wave field is imposed upon the ambient medium and the scatterer. The scattered field is measured at detectors placed a finite distance from the scattering objects. The material parameters of the scatterer are then reconstructed from the information contained in the incident and scattered fields. In other words, as defined herein, acoustic or electromagnetic imaging using inverse scattering techniques is intended to mean electronic or optical reconstruction and display of the size shape, and unique distribution of material elastic or electromagnetic and viscous properties of an object scanned with acoustic, electromagnetic or acoustic energy, i.e., reconstruction of that scattering potential which, for a given incident field and for a given wave equation, would replicate a given measurement of the scattered field for any source location.
The description of prior art summarized in U.S. Pat. No. 4,662,222 (referred to as "the previous Patent") is also relevant here. It is sufficient to say here, that the use of the conjugate gradient algorithms discussed in the previous patent brought the attainment of inverse scattering into a practical reality. Previous to that U.S. Pat. No. (4,662,222), only linear approximations to the full inverse scattering problem were amenable to solution, even with the aid of modern high speed digital computers. The resolution achievable with the inverse scattering methods described in the previous patent was far superior to any ultrasound imaging in medicine previous to that time,